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y=e^(arctg^2√(2x-1))
Derivada de la función/ (2x-1)/ ctg^2/ arctg/ y=e^(arctg^2√(2x-1))

Derivada de y=e^(arctg^2√(2x-1))

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     2      _________
 atan (x)*\/ 2*x - 1 
E
e2x−1atan⁡2(x)e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}} 
E^(atan(x)^2*sqrt(2*x - 1))
Gráfica
02468-8-6-4-2-1010020000
Trazar el gráfico f(x)
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Primera derivada [src] 
/      2           _________        \      2      _________
|  atan (x)    2*\/ 2*x - 1 *atan(x)|  atan (x)*\/ 2*x - 1 
|----------- + ---------------------|*e                    
|  _________                2       |                      
\\/ 2*x - 1            1 + x        /
(22x−1atan⁡(x)x2+1+atan⁡2(x)2x−1)e2x−1atan⁡2(x)\left(\frac{2 \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{\sqrt{2 x - 1}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}
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Segunda derivada [src] 
/                               2                                                                                             \                       
|/                   __________\                    2            __________                                 __________        |    __________     2   
||  atan(x)      2*\/ -1 + 2*x |      2         atan (x)     2*\/ -1 + 2*x          4*atan(x)         4*x*\/ -1 + 2*x *atan(x)|  \/ -1 + 2*x *atan (x)
||------------ + --------------| *atan (x) - ------------- + -------------- + --------------------- - ------------------------|*e                     
||  __________            2    |                       3/2             2      /     2\   __________                  2        |                       
|\\/ -1 + 2*x        1 + x     /             (-1 + 2*x)        /     2\       \1 + x /*\/ -1 + 2*x           /     2\         |                       
\                                                              \1 + x /                                      \1 + x /         /
(−4x2x−1atan⁡(x)(x2+1)2+22x−1(x2+1)2+(22x−1x2+1+atan⁡(x)2x−1)2atan⁡2(x)+4atan⁡(x)2x−1(x2+1)−atan⁡2(x)(2x−1)32)e2x−1atan⁡2(x)\left(- \frac{4 x \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right)^{2} \operatorname{atan}^{2}{\left(x \right)} + \frac{4 \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}
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Tercera derivada [src] 
/                               3                                                                                                                                                                                                                                                                                                              \                       
|/                   __________\                     2                                       __________                                __________             /                   __________\ /       2            __________                                 __________        \                                        2   __________        |    __________     2   
||  atan(x)      2*\/ -1 + 2*x |      3        3*atan (x)              6              12*x*\/ -1 + 2*x          6*atan(x)          4*\/ -1 + 2*x *atan(x)     |  atan(x)      2*\/ -1 + 2*x | |   atan (x)     2*\/ -1 + 2*x          4*atan(x)         4*x*\/ -1 + 2*x *atan(x)|                12*x*atan(x)        16*x *\/ -1 + 2*x *atan(x)|  \/ -1 + 2*x *atan (x)
||------------ + --------------| *atan (x) + ------------- + ---------------------- - ----------------- - ---------------------- - ---------------------- - 3*|------------ + --------------|*|------------- - -------------- - --------------------- + ------------------------|*atan(x) - ---------------------- + --------------------------|*e                     
||  __________            2    |                       5/2           2                            3       /     2\           3/2                 2            |  __________            2    | |          3/2             2      /     2\   __________                  2        |                   2                                3         |                       
|\\/ -1 + 2*x        1 + x     /             (-1 + 2*x)      /     2\    __________       /     2\        \1 + x /*(-1 + 2*x)            /     2\             \\/ -1 + 2*x        1 + x     / |(-1 + 2*x)        /     2\       \1 + x /*\/ -1 + 2*x           /     2\         |           /     2\    __________           /     2\          |                       
\                                                            \1 + x / *\/ -1 + 2*x        \1 + x /                                       \1 + x /                                             \                  \1 + x /                                      \1 + x /         /           \1 + x / *\/ -1 + 2*x            \1 + x /          /
(16x22x−1atan⁡(x)(x2+1)3−12x2x−1(x2+1)3−12xatan⁡(x)2x−1(x2+1)2−42x−1atan⁡(x)(x2+1)2+(22x−1x2+1+atan⁡(x)2x−1)3atan⁡3(x)−3(22x−1x2+1+atan⁡(x)2x−1)(4x2x−1atan⁡(x)(x2+1)2−22x−1(x2+1)2−4atan⁡(x)2x−1(x2+1)+atan⁡2(x)(2x−1)32)atan⁡(x)+62x−1(x2+1)2−6atan⁡(x)(2x−1)32(x2+1)+3atan⁡2(x)(2x−1)52)e2x−1atan⁡2(x)\left(\frac{16 x^{2} \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)^{2}} - \frac{4 \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right)^{3} \operatorname{atan}^{3}{\left(x \right)} - 3 \left(\frac{2 \sqrt{2 x - 1}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1}}\right) \left(\frac{4 x \sqrt{2 x - 1} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \sqrt{2 x - 1}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \operatorname{atan}{\left(x \right)}}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}}\right) \operatorname{atan}{\left(x \right)} + \frac{6}{\sqrt{2 x - 1} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{5}{2}}}\right) e^{\sqrt{2 x - 1} \operatorname{atan}^{2}{\left(x \right)}}
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Gráfico
Derivada de y=e^(arctg^2√(2x-1))
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